THE CONSTITUTION OF NATURE. 23 



tance from F, Ave can in imagination draw a straight line 

 from D to F, and at D erect a perpendicular to this line, 

 which shall represent the amount of the attraction exerted 

 on D in this position. If D be at a very great distance 

 from F the attraction will be very small, and the perpendic- 

 ular consequently very short. Let us now suppose that at 

 every point in the line joining F and D a perpendicular is 

 erected proportional in length to the attraction exerted at 

 that point ; we should thus obtain an infinite number of 

 perpendiculars of gradually increasing length as D ap- 

 proaches F. Uniting the ends of all these perpendiculars, 

 we should obtain a curve, and between this curve and the 

 straight line joining F and D we should have an area con- 

 taining all the perpendiculars placed side by side. Each 

 one of this infinite series of perpendiculars representing an 

 attraction, or tension as it is sometimes called, the area just 

 referred to represents the total effort capable of being ex- 

 erted by the tensions upon the particle D, during its pas- 

 sage from its first position up to F. 



Up to the present point we have been dealing with ten- 

 sions, and not with motion. Thus far vis viva has been 

 entirely foreign to our contemplation of D and F. Let us 

 now suppose D placed at a practically infinite distance from 

 F ; here the pull of gravity would be nothing, and the per- 

 pendicular representing it would dwindle to a point. In 

 this position the sum of the tensions capable of being ex- 

 erted on D would be a maximum. Let D now begin to 

 move in obedience to the attraction exerted upon it. Mo- 

 tion being once set up, the idea of vis viva arises. In 

 moving toward F the particle D consgmes, as it were, the 

 tensions. Let us fix our attention on D at any point of the 

 path over which it is moving. Between that point and F 

 there is a quantity of unused tensions ; beyond that point 

 the tensions have been all consumed, but we have in their 

 place an equivalent quantity of vis viva. After D 1ms 



